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CARBON CYCLE MODELLING: ILLUSTRATIONS OF MODELLING PROBLEMS IN IGBP STUDIES

I.G. Enting

10 INTRODUCTION

The International Geosphere-Biosphere Program (lGBP) is a proposed multi-disciplinary

study of the geosphere-biosphere system. The various elements of this system are the

atmosphere, hydrosphere, terrestrial and aquatic biota, soils and sediments. The main

dements of the IGBP defined in the 1986 ICSU report [1] are:

iii Studies of interactive processes that govern global change.

II Development of a new generation of coupled models of the environment.

O!I Design of suitable tests to guide the development of these models and the under-

standing of the processes.

Oil Programs of observations tailored to provide data needed for these activities.

The present report explores some of the issues involved in modelling and other theoretical

studies within the IGBP. The perspective reflects the author's experience in atmospheric

science; the global carbon cycle is used to illustrate many of the issues.

The proposed IGBP core projects include two modelling projects: Modelling Global

Biogeochemical Cycles and Geosphere-Biosphere Models [2]. The biogeochemical mod-

elling is introduced as a guide to the more complicated geosphere-biosphere modelling

and because the carbon cycle in particular will 'be the core element of any truly global

geosphere-biosphere model' [2].

Air Chemistry

Marine chemistry

Marine biota

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Soils

Land biota

Atmospheric Physics i-----------oj

Cryosphere

Ocean Physics l I

Figure 1: Schematic representation of major components of the geosphere-biosphere sys­tem.

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The IGBP is an attempt to obtain an overall view of global change as an alternative to

piecemeal approaches that have been used to date. Most studies of aspects of global change

have been on a problem-by-problem basis, e.g. ozone depletion by supersonic transports,

ozone depletion by nuclear testing, ozone depletion by chloro:ll.uorocarbons, the ozone

hole, the CO2 greenhouse effect and the augmenting of the greenhouse effect by methane

and chloro:ll.uorocarbons. The proposed US Global Tropospheric Chemistry Program [3]

is designed to give a degree of understanding of atmospheric chemistry that is adequate

for dealing promptly with new concerns as they arise. In the area of ocean chemistry

and dynamics a series of integrated programs such as GEOSECS, TTO and the proposed

World Ocean Circulation Experiment (WOCE) [4] have been developed to provide data

bases for ocean modelling. These integrating programs have been within single disciplines.

The IGBP aims to take the process one step further and integrate different disciplines. The

aim of this integrative activity could be regarded as Lovelock's 'Geophysiology' which he

refers to as 'the earth science' (singular) rather than the traditional terminology of 'earth

sciences' (plural) [5].

In the description of the elements of the IGBP, the key word is 'interactive'. It is the

interaction between the various components of the geosphere-biosphere system than make

a multi-disciplinary approach necessary. Interaction between the various components of

the system allows the possibility of complex feedback loops.

The importance of identifying the feedbacks in the system can be demonstrated by

comparing two extreme views of the system. The first view is the tra.ditional single­

discipline approach in which the various components shown in Figure 1 are studied indi­

vidually, generally at a finer level of description than the lumped form used in Figure 1.

In such studies, the other components are regarded as a specified environment (often fixed

in time) that ads on the subsystem of interest but which is not significantly influenced

215

in return. In the absence of feedback loops such an approach could be used to obtain a

description of the behaviour of the system as a whole.

An alternative to the 'single-discipline' view of the geosphere-biosphere system is em­

bodied in the 'Gaia' hypothesis of Lovelock [6J. This approach regards the biota as

controlling the composition ofthe atmosphere in such as way as to preserve the habitibil­

ity of the planet in the face of perturbing influences. In later work, Lovelock [5J has

noted that in systems where such negative feedback leads to homeostasis, it is frequently

possible for the feedback processes to 'saturate' so that a sufficiently strong perturbing

influence can overwhelm the controls and cause the system to change abruptly to some

new state. Broecker [7J has warned that the relation between CO2 content and deposition

temperature obtained from polar ice-cores indicates that such an instability may occur

in the subsystem involving the dynamics and CO2 content of the atmosphere and the

dynamics and carbon content of the oceans.

The bulk of this report (Sections 4 to 7) explores various problems that can be expected

in modelling the geosphere-biosphere system. Section 2 lists these problems. Some of them

were identified in the 1986 ICSU report [IJ. Others are suggested by experience in the

development of atmospheric composition studies and carbon cycle studies in particular.

Carbon cycle modelling is discussed in Section 3; it is used to illustrate many of the

problems that are discussed.

Sections 4, 5, 6 and 7 explore, respectively, the problems of different model type,

mismatch in time- and space-scales, the difficulties of ill-posed problems and the possibility

of new modes of chaotic behaviour. Section 8 reviews some significant problems involving

linkages between different components of the geosphere-biosphere system.

2. PROBLEMS

The 1986 ICSU report [1] identified two important problems in the study of the geosphere­

biosphere system:

~ The differences between the spatial scales usually involved in studies of individual

components of the system.

!II Differences in the time-scales involved in the various components.

There are, a nmnber of other methodological that can be expected

when undertaking studies of the geosphere-biosphere system:

@I Many studies are going to involve the solution of ill-posed problems in which one is

trying to deduce properties that are extremely sensitive to smaH errors in measure­

ments and sman uncertainties in our knowledge of the system behaviour.

@ There is a severe mismatch between the types of model possible for the different

components of the geosphere-biosphere system. Karplus [8] suggested classification

of models along a spectrum ranging from 'black-box' curve-fitting models through

to 'white-box' fully-deductive models. Currently models of various components of

the geosphere-biosphere system range right across this modelling spectrum.

II It is possible that the existence of the feedback loops shown in Figure 1 allows

the system to exhibit new modes of chaotic dynamics that are additional to the

chaotic behaviour that occurs in individual components of the system. Such chaotic

behaviour is a quasi-random evolution of deterministic systems. Chaotic behaviour

has been extensively studied, especially in connection with the theory of turbulence

and so is well known in atmospheric and oceanic dynamics. A number of key

references were collected by Cvitanovic [9].

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Reservoir Size, Gt C Turnover, y Rate of change Atmosphere 614 4 3 Land biota ~700 ~10 ? Soils ::::;1500

Ocean surface 1000 ::::;8 ~O.5

Deep oceans 30000 > 100 ? Fossil fuel 7000 ? -5 Reactive CaC03 sediments 2500 10000 ? CaC03 3 X 107 101 ?

Table 1: The main reservoirs involved in the global carbon cycle, together with current carbon contents (in Gt C), and turnover time and net carbon exhanges (in Gt C y-l)

@ The development of the 'new generation of coupled models' is to encounter

considerable difficulty and require new methodologies for calibrating and validating

models when the calibration process is inherently ill-conditioned and the system

may exhibit chaotic dynamics.

These vanons difficulties are described in more detail in subsequent sed ions , and

illustrated by relevant examples from previous studies of the carbon cycle and other com-

ponents of the geosphere-biosphere system. It is important ~o note this list of problems is

based on such experience. The possibility remains that studies of the geosphere-biosphere

system may encounter fu:rther methodological problems that are qualitatively different

from any encountered in the study of particular subsystems.

30 CARBON CYCLE MODELLING

Table 1 lists the various components involved in the global carbon cycle, and using data

based on the study by Sundquist [10] gives the approximate size of the carbon reservoirs,

their estimated rates of change ( i.e. net flux into the reservoir) and their turnover times,

defined as the ratio of reservoir size to gross carbon exchanges with other reservoirs.

Three-dimensional models of atmospheric transport have been used to look at the

seasonal variation of CO 2 [11]. These models compute the transport using either met eo-

218

rological data or else the transport fields calculated by a general circulation model (GCM)

of atmospheric dynamics. Ocean general circulation models have been used to calculate

the uptake of CO2 into the deep oceans [12]. Because of the very different time-scales in­

volved in the atmosphere and the ocean, these two types of GCM-based transport models

of aspects of the carbon cycle have not been run coupled together and it seems inappro­

priate to do sOi in each case a parameterised form of the other model's behaviour can be

used as a boundary condition of the other.

Two-dimensional models of atmospheric transport are more flexible than the corre­

sponding three-dimensional models. In particular it is possible to run such models in an

inverse mode, specifying a zonally averaged surface CO2 concentration and calculating

the corresponding surface sources [13, 14). When run in this mode, the models can be run

as 'atmosphere-only' models. When atmospheric transport models are nm in the forward

mode, the surface sources need to be specified. At the very least, an ocean surface model

is needed as in the work of Pearman and Hyson [15]. Even in this case the treatment of

transfer of carbon into the sub-surface layers of the ocean must be parameterised in some

way.

Traditionally the combined global carbon system in the atmosphere, the oceans and

the land biota has been modelled using coarse lumped 'box-models' [16, 17]. These are

used to study changes on time-scales of decades to centuries. Sundquist [10J presents a

range of models of this type, including several thai include the carbonate sediments and

which are therefore applicable to geological time-scales.

40 THE MODELLING SPECTRUM

Karplus [8] defined a spectrum of mathematical modelling according to the amount of

inductive as opposed to deductive information embodied in the models. This spectrum

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Quantity Reservoir Space Time interval Coverage CO2 conc Atmosphere 30 sites $ 1 mouth ~1980 onwards CO2 conc Atmosphere 2 sites $ 1 month 1958 onwards CO2 conc Air in ice several sites ~10 y 1700 - present CO2 conc Air in ice few sites ~1000 y 160000 BP to present 13C:12C Atmosphere Several sites $ 1 month last 5 years 14C:12C Atmosphere Several sites ~1 month 1960 - present 14C:12C ocean surface Several regions $ 1 month 1906 on 14C:12C Ocean Few cross sections one-off 1973 14C:12C Tree rings Many sites $5y several centuries

Table 2: Typical data for carbon cycle modelling

runs from fully-inductive 'black-box' modelling through various shades of grey to fully-

deductive 'white-box' models. One important property associated with the spectrum is

the range of validity of a model. An inductive model can only be expected to be valid

for those conditions from which it was calibrated. In contrast, models that are developed

by systematic deduction from general physical laws can be expected to be valid over the

whole domain of applicability of such laws.

Karplus noted that particular subject areas tended to occupy specific positions on the

modelling spectrum. However, a contrasting viewpoint was given by Enting [18] who gave

examples of aspects of the carbon cycle using models spanning virtually the whole range

of the modelling spectrum.

As noted in Section 2, the models that have usually been applied to individual com-

ponents of the geosphere-biosphere system have come from widely scattered points on the

modelling spectrum. A few examples will illustrate the range.

Atmospheric dynamics In principle the dynamical behaviour of the atmosphere is

close to being a white-box system. The behaviour of the atmosphere is governed by basic

physical laws: Newton's laws of motion, the equation of state for air as a function of

moisture content and laws of radiative transfer. The boundary conditions at the earth's

surface, involving friction, radiation and exchange of water pose some difficulties. One of

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the most serious difficulties in modelling atmospheric dynamics is that the spatial scale of

atmospheric motions ranges from turbulent motions on the scale of metres to organised

hemispheric circulations with corresponding variations in time scales of minutes to years.

Because of the non-linear interactions, the effects of such sub-grid scale turbulence must

be parameterised empirically. Another parameterisation is involved in the description of

cloud cover in global-scale models, because douds generaHy form on scales smalJer than

any currently realistic grid-scale. Empirical parameterisations can be derived indudively

a,s noted above, this can limit the extent to which the model can be applied under

different climatic conditions. The questions of whether such parameterisatiolls remain

valid under changed climatic conditions represents one of the major doubts concerning

the applicability of general circulation models of the atmosphere to studies of climatic

change. In spite of these problems, general circulation models of the 1l.l,mosphere are dose

to the 'white-box' end of the spectrum.

Atmospheric chemistry Modelling the behaviour of chemically active constituents of

the atmosphere is subject to a number of difficulties. Almost invariably very large numbers

of distinct chemical reactions are taking place and often the rate constants (and their

dependence on temperature) are poorly known. It is generally necessary to truncate the

system to 100 or so reactions without there being any systematic technique for evaluating

the importance of those reactions that are excluded. The unpredicted appearance of the

so-caned 'ozone-hole' is an example of the surprises that may be in store in this area.

(The 'ozone-hole' is apparently the result of chemistry on ice in polar stratospheric clouds

~ such inhomogeneous processes had not been included in atmospheric models at the

time the hole was detected.)

Ocean dynamics The development of ocean general circulation models from first prin­

ciples is at a less developed stage than the development of general circulation models of

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the atmosphere. There are a number of reasons for tIus. One is that both temperature

and salinity variations give density changes that can drive ocean circulation. A more

important difference is the smaller scale of the most dynmaically important eddies. This

not only makes modelling more difficult but also has the further effect of limiting the •

representativeness of observational records which are in any case far sparser than the

corresponding atmospheric records.

A consequence of the difficulties involved in modelling the circulation of the ocean

is that most studies of ocean chemistry have used highly simplified parameterisations of

ocean transport of minor constituents. A prominent example is the 'box-diffusion model"

of Oeschger et al. [16] which was developed for global carbon cycle studies. This model

simply represents the world ocean as a single, spatially uniform surface layer overlying a

water mass with purely diffusive transport. This approach to modelling ocean uptake of

atmospheric constituents corresponds very much to a grey-box region of the spectrum of

models. It is not entirely inductive since it is assumed that different tracers can be taken

up in similar ways. In particular, these models are often calibrated using the response

to the 14C from nuclear tests. Broecker et al. [19] suggested recalibrating the diffusion

parameter on the basis of tritium from thermonuclear weapons tests.

At the 'black-box' end of the spectrum, statistical modelling has an important role.

Much of the analysis of the carbon cycle uses signals that have been obtained by statistical

processing of observational data (often as time series). Proper statistical analysis and

processing requires the use of a statistical model (either implicitly or explicitly) and such

models need to be validated for that task. This is not often done in studies of atmospheric

composition. For CO2 , the WMO Hilo meeting [20] represents a useful step towards a

sounder approach to statistical analysis.

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5, MISMATCH BETWEEN SPACE AND TIME SCALES

The differences in space and time scales between the various components of the geosphere­

biosphere system was noted as a problem in the 1986 ICSU report [1], There is already

a large body of experience with problems of discordant time scales that should give some

guidance in dealing with these problems. Hopefully some of the techniques can be used

to deal with mismatched space-scales. Various previo!lsly studied contexts in which dis-

cord ant time-scales are involved are:

the large variations in rate constants for chemical reactions. In some cases these problems

can be handled by numerical techniques designed for 'stiff' differential equations. In other

cases the behaviour can be approximated by assuming that a set of 'fast' reactions can

always be regarded as having proceeded to equilibrinm and then the resulting equilibrium

conditions can be used to specify the concentrations of constituents involved in the 'slow'

reactions.

lHmospheric dynamics There are a number of contexts in which problems in atmo­

spheric dynamics involve a very wide range of time scales. As an example, Holton [21]

describes how numerical forecasting calculations have to remove the fastest dynamical

modes of the atmosphere (sound and gravity waves) anow sufficeintly large time step in

the numerical solution.

The global carbon cycle Sundquist [10] presents an analysis of an hierarchial series

of carbon cycle models describing the periods ranging from decadal time scales for the

atmosphere/ocean/biosphere system through to time-scales of 105 years or longer. A

matrix-eigenvector analysis was used to relate various models in the sequence which were

derived by successive combination of reservoirs.

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In general the mis-match between space and time scales becomes important when

non-linear interactions are involved - for linear interactions, we can work with averages.

Unfortunately some of the most strongly non-linear interactions occur between the biota

and the atmosphere (both physical and chemical) where much of the atmospheric influence

comes from relatively rare extreme events.

6. ILL-CONDITIONED INVERSE PROBLEMS

There has been an 1"'0":;',,"Jl1&,''\ recognition of the importance of ill-conditioned inverse prob-

lema in studies of many cornponents of the geosphere-biosphere system. In appreciating

the role of inverse it is necessary to make a distinction between descriptive or

forward modelling as opposed to deductive or inverse modelling. In this context, 'de­

ductive' refers to the way the model is used whil in Section 4, it refers to the way the

model is constructed. Thus forwardmodelling is involved with the 'whiter' end of the

modelling spectrum defined in Section 4 above. A system is modelled by assuming a com­

plete specification of all the model processes and the outputs are compared to real-world

observations. In inverse modelling, some or aU of the processes are incompletely specified

and the comparison between the model outputs and real-world observations is used as a

basis for adjusting the model until agreement is reached. Allison [22] has described the

reasons why this deductive inverse approach is potentially unstable. The argument is that

for numerical or mathematical modelling to be practical, the system must be such that it

can be usefully approximated. The outputs of the model must be relatively insensitive to

incompleteness or inaccuracy in the model specifications and to incompleteness or errors

in the inputs driving the model. Relatively large amounts of error or incompleteness in

both the model and its inputs should give only smaH changes in the outputs. It follows

that if a model with these properties is being used in the inverse mode of determining

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aspects of the model structure or its inputs from a comparison between observations and

model outputs then small amounts of error or incompleteness in the observations will lead

to large errors in the quantities determined in the inverse calculation. Allison [22J noted

that in mathematical terms, the ability to sensibly approximate a system corresponds to

the requirement that the behaviour of the system be described by a compact operator.

The difficulties with the inverse problem arise from the fact that no compact operator has

a bounded inverse.

Craig and Brown [23J discuss the methodological problems of fields of study in which

inverse problems are common. It is usually the case that if only indirect information is

available about some physical system then only a projection of lhe system's characteristics

will be obtainable. A description of a general mathematical approach to the linear inverse

problem is given by Jackson [24J. Techniques for dealing with ill-conditioned inverse

problems are wen-advanced in seismology and other fields involving remote sensing [25].

There is also a significant history of using temperature and salinity variations to deduce

ocean circulation. A more recent biogeochemical study attempted to use multiple tracers

to determine the broad scale features of ocean circulation [26]. This attempt encountered

some consistency problems involving phosphorus distributions. Mansbridge and Enting

[27] re-examined the calculations to see whether the problem might have arisen from

insufficient smoothing but they concluded that the problem must lie in some limitation

of the model.

In the time-domain the most common inverse problem is the deconvolution problem.

For a linear system the amount of tracer remaining in a reservoir such as the atmosphere

at a time t after a unit impulse source is given by a response function R( t). This allows

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one to relate the time history of concentrations c(t) to a time history of sources by

(1) c(t) = c(to) + l R(t - t')s(t')dt'.

Enting and Mansbridge [28] discussed the inversion of (1) in connection with the inter­

pretation of CO2 data from ice-cores [29]. In particular they noted:

(i) there is an explicit inversion relation of the form

(2) s(t) = c(t)/ R(O) + (c(t) - c(O))R(O)/ R(0)2 -l K(t - t')[c(t') - c(O)]dt'

where K(t) is a smoothly varying inversion kernel.

(ii) the instability in the inversion arises solely from the occurrence of a derivative of

c(t) in the first term of (2);

(iii) approximating R(t) by sums of exponentials leads to K(t) being also a sum of

exponentials.

(iv) the inversion relation (2) shows clearly how uncertainties about past CO2 concen­

trations will influence estimates of present CO2 sources.

For spatial problems a greater diversity of inverse problems occurs; some of these were

discussed by Enting (1985). A more comprehensive analysis is given by Newsam and Ent­

ing (1988). They considered the problem of deducing surface sources of a tracer such as

CO2 from measurements of atmospheric concentrations approximating atmospheric trans­

port as a purely diffusive process. They found that the the noise amplification depends

roughly linearly on the wave number k. Enting [30] and Enting and Mansbridge [13] noted

the linear k-dependence for inversions using a two-dimensional advective-diffusive model.

Newsam and Enting [31] also considered the inversion of high-altitude data e.g. upper

troposphere CO2 data. The inversion problem is worse-conditioned than any order of

differentiation: the noise amplification grows as [ksinh(k)p/2. Thus, the concentrations

are only significantly affected by the global-scale features of the sources. Therefore, so

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long as the inversion is constrained to produce only such global-scale features, they can

be deduced without being concerned about interference from smaller-scale details. Enting

and Newsam [32] also considered the extent to which ground-based observations can give

information about processes in the free atmosphere.

Enting [33] and Enting and Pearman [34J have pointed out the poorly-conditioned

nature of the calibration of carbon cycle models - often the data are insufficient to

distinguish between alternative processes. They used a Bayesian approach to model cali­

bration. Another interesting aspect of that work (see also [35]) was their use of the models

to analyse the extent to which new observations could resolve the uncertainties. They did

this by performing model calibrations, combined with sensitivity studies while including

various items of 'hypothetical data' to see if such data could reduce the sensitivity of

the modeL Since we can expect many aspects of the geosphere-biosphere system to be

poorly-defined, this type of modelling may be used to plan observational programs and

therfore could playa key role in the IGEP.

7. CHAOTIC DYNAMICS

In recent years it has been recognized that many deterministic dynamical systems can

exhibit apparently random behaviour. This can occur in quite simple systems: the mini­

mum requirements are three first-order differential equations with a non-linear coupling.

A classic example of this type is given in the study by Lorenz [36). In such chaotic

systems states that are dose initially tend to diverge exponentially with time implying

that the detailed evolution of the system is essentially unpredictable after some char­

acteristic period. Lorenz [37) has studied the implications of this type of behaviour on

the limits of weather forecasting; the existence of chaotic behaviour in the atmsophere

places very severe limita.tions on our ability to predict the wea.ther at a specified time.

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However this limitation does not automatically make it impossible to compute climatic

averages under either present or future climatic forcing. A more serious problem for the

prediction of climatic change is the role of chaotic behaviour in the ocean or in the com­

bined atmosphere-ocean system. The role of such variability is currently unclear. The

field of chaotic is currently an extremely active field of research 1U

connection with the problems of turbulence.

'Within the geosphere-biosphere system it is obvious that chaotic dynamics occurs in

many of the individual components. The atmosphere has already been noted. Turbulent

eddies also an important role in the oceanic circulation. Chaotic dynamics can also

occur in biotic systems of the predator-prey type. If, as is common, time-lagged interac­

tions are considered as representing the maturing of individuals then chaotic behaviour

can occur with fewer than three components [38J.

As implied the

known in many of the relevant

given above, this chaotic behaviour is relatively wen·

areas. The most important question for the IGBP

is whether coupling the various subsystems allows any new modes of chaotic behaviour

as opposed to merely

systems.

the parameters describing the behaviour of individual sub·

The behaviour of the carbon itself, seems to be too highly damped to support

chaotic oscillations. There is however, a suggestion Ghil [39] that chaotic behaviour

may be involved with the interactions between CO 2 and climate. The feedback path is

discussed further in the following Section but it may be summarised as 'climate affects

ocean circulation which affeds ocean chemistry which affects atmospheric CO 2 which

affects climate'. This feedback provides a way of amplifying the relatively weak radiative

effects of variations in the earth's orbit to a sufficient degree to cause the ice ages. Ghil

suggests that the natural behaviour of this interacting system could be some form of

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chaotic behaviour so that the astronomical forcing would produce a response that varied

from one time period to the next. This suggestion could give an explanation of some of

the anomalies observed in the relation between paleoclimatic records and the astronomical

cycles. The firsi anomaly is that the relations are apparent in the frequency domain but

are less obvious in the time domain - this could be expected if the behaviour of the

system corresponded to periodic forcing of a chaotic oscillator. The second anomaly is

thai the relative importance of the vario1lls frequencies in the paleo-climatic record does

not reflect the ordering of the relative radiative effects of the astronomical variations -

again this could be explained by reference to the instrinsic dynamics of the CO,-climate

system.

g, CURRENT PROBLEMS

A problem of current concern is the possibility of a dosed feedback loop in the CO2

climate connection. Such a possibility is suggested by the fact that CO2 concentrations

(as determined from bubbles trapped in polar ice) were typically 200 ppmv during glacial

periods. Since CO 2 is an important greenhouse gas, this result implies that the reduction

in CO2 contributed to the lowering of temperatures. However the correspondence between

glacial periods and the characteristics of the earth's orbit suggest a primary astronomical

forcing (subject to the qualifications in the previous section). The CO 2 feedback can

resolve the problem that orbital changes alter the radiation input to the earth by an

amount that is insufficient to account for the temperature differences between glacial and

interglacial periods. In addition, the attribution to CO2 of a major role in the glacial

inter-glacial cycle explains why glaciations were synchronous between the hemispheres

even though the primary astronomical forcing had opposing phases in each hemisphere.

Various mechanisms have been proposed for the lowering of CO2 • Currently the most

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plausible involve changes of ocean circulation giving changes of ocean nutrient balance

causing changes in the marine biota and thus in the carbon distribution in the ocean

surface and the atmosphere.

This feedback is of current concern for two related reasons. Firstly, a positive feedback

between CO2 and climate could amplify the greenhouse effect due to fossil fuel use. Sec­

ondly there is a growing body of evidence that the ocean circulation has at times changed

quite abruptly, particularly around the end of the last glaciation. It is thus conceivable

that sucll abrupt changes could occur in response to anthropogenic CO2 • As noted above,

such abrupt change can be characteristic of the response of homeostatic systems when

subjected to a forcing that exceeds the adaptive limits of the system.

In connection with these problems, an important question is whether the ocean cir­

culation and chemistry is currently represented by an equilibrium steady state plus. a

chemical perturbation from fossil carbon. There are a number of aspects of this question

that suggest further investigation. Firstly, Enting and Mansbridge [40] showed that there

was no possible linear steady-state ocean model that could reconcile the biotic CO2 release

estimates by Houghton et al. [41] with a history of CO2 concentrations from ice cores ob­

tained by Neftel et al. [29]. Enting and Mansbridge favoured the explanation that biotic

release estimates were either in error or missing some processes but noted the possibility

of a time-varying ocean circulation, possibly representing a recovery from lit,tIe ice-age

conditions. Given the importance of phosphorus in many theories of the climate-C02

feedback it is interesting to note that the multi tracer inversion of Bolin et al. [26] (which

assumed a steady-state ocean circulation) had most difficulty accounting for the observed

phosphorus distribution. Further theoretical studies of these questions seem desirable. In

addition it would be valuable to conduct more detailed studies using ice-cores to establish

CO2 changes through the onset, duration and recovery from the little ice-age. Such a

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study might provide an example of the climate COrfeedback as well as helping answer

the question of whether the ocean circulation and chemistry is in a steady state; (ii)

still recovering from changes connected with the little ice age, or (iii) responding to cli­

matic consequences of the increases in CO2 , This last possibility seems unlikely at present

given the lack of clear detection of a CO 2-induced increase in atmospheric temperature.

However it is a possibility that must be given increasing consideration as time goes on.

A recent study that raises the possibility of such changes is that of Tans et aL [42].

Their argument has three main steps;

OJ Inversion of atmospheric CO 2 data suggests that the southern oceans are only a

weak sink of CO2 (in proportion to their area) while there is a strong sink at mid

latitudes of the northern hemisphere

\l) Ocean PC02 data indicates that northern oceans are not a strong CO2 sink, implying

that the sink must be in the terrestrial biota

~ Integration over the oceans gives a net sink of 0.5 to 1.0 Gt C y-l

There are three distinct interpretations of these results:

Ii The analysis is incorrect.

Oil The oceans have always been a weak sink of CO 2 . This seems to be inconsistent

with radiocarbon data from the period after nuclear testing unless some key process

has been neglected.

II The oceanic uptake has changed so that the oceans are taking up less CO 2 than

previously.

One fact that points towards a possible change in oceamc CO 2 uptake is that the

modelling study by Pearman and Hyson (1986) found that the atmospheric CO2 data

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were consistent with the southern oceans being a strong sink while the studies by Enting

and Mansbridge [13J and Tans ei al. [14] indicated a weak southern ocean sink. While there

were important differences between the models used, a major determinant of the differing

conclusions was differences in the CO, data. The earlier data analysed by Pearman and

Hyson [15J had a much greater change between the south pole and the equator than was

apparent in the later data. This may indicate a genuine change but it could equally well

reflect calibration problems in the earlier records.

90 CONCLUSIONS

The conclusion of this review is that theoretical studies within the IGBP will require the

development of new methodologies for modelling. There is a need for development in the

fields of numerical modelling, mathematical analysis and statistical modelling.

The development in numerical modelling must deal with the problems of mismatches

in space and time scales. Mathematical analysis is needed as a guide to the appropriate

use of numerical models. In the area of fluid dynamics of the atmosphere and ocean there

is a large body of analytic work that can provide paradigms for interpreting the behaviour

of numerical nwdels in terms of such concepts as internal gravity waves, Rossby waves,

Kelvin waves, etc. In other fields such as atmospheric chemistry such a tradition is lacking

although simplified low-resolution models can be of some use in interpreting the results

of large numerical models.

10. ACKNOWLEDGEMENTS

The author wishes to acknowledge valuable comments on the manuscript from many

colleagues.

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